3
$\begingroup$

what is the criterion for a random variable(continous) for existence of probability density function for it? Could you provide some cases of random variable(continous) where pdf ceases to exist.

$\endgroup$
  • 1
    $\begingroup$ How are you defining a continuous random variable? $\endgroup$ – M. Vinay Jun 19 '14 at 5:17
  • 4
    $\begingroup$ Sometimes "continuous random variable" means "random variable with a density function." $\endgroup$ – Qiaochu Yuan Jun 19 '14 at 5:18
  • $\begingroup$ a continous random variable has continous CDF function. $\endgroup$ – VKV Jun 19 '14 at 5:18
  • 2
    $\begingroup$ It happens if the cdf is absolutely continuous. $\endgroup$ – André Nicolas Jun 19 '14 at 5:20
  • 4
    $\begingroup$ An example in which it is not absolutely continuous is en.wikipedia.org/wiki/Cantor_distribution $\endgroup$ – M. Vinay Jun 19 '14 at 5:22
0
$\begingroup$

A (real-valued) random variable $X$ has density $f$ if you can write $$P(X \leq x) = \int_{-\infty}^x f(y) dy$$.

For a random variable which does not admit a density, take any discrete random variable - geometric, bernoulli, etc.

$\endgroup$
  • $\begingroup$ i want to know whether every continous random variable has a density function or not. thanks $\endgroup$ – VKV Jun 19 '14 at 5:13
  • $\begingroup$ This answer is off-topic, the OP is basically asking about random variables of the third type, neither absolutely continuous nor discrete. $\endgroup$ – Did Jun 19 '14 at 5:51
  • $\begingroup$ This answer was on topic for the original question. $\endgroup$ – Batman Jun 20 '14 at 2:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.